Movies for PDE

Movies for Partial Differential Equations

Transport equation: u_t + u_x = 0

Transport with decay: u_t + u_x + u = 0

Nonuniform Transport: u_t + u_x / (x² + 1) = 0

Nonuniform Transport: u_t + (x² - 1) u_x = 0

Nonlinear Transport: u_t + u u_x = 0, straight line solutions

Nonlinear Transport: u_t + u u_x = 0, rarefaction wave

Nonlinear Transport: u_t + u u_x = 0, shock wave

Shock wave solution

Multi-valued solution corresponding to the shock wave

Equal area rule for shock wave

Nonlinear Transport: u_t + u u_x = 0, initial step function

Rarefaction wave

Shock wave

Multi-valued solution corresponding to the shock wave

Equal area rule for shock wave

Heat equation: u_t = u_xx, Dirichlet boundary conditions

Heat equation: u_t = u_xx, periodic boundary conditions

Heat equation: u_t = u_xx, denoising

Wave equation: u_tt = u_xx, particles and waves

The wave solution u(t,x) = cos t sin x = (sin(x-t) + sin(x+t))/2

Constitutent traveling waves (particles)

Particles and Waves

Wave equation: u_tt = u_xx, interaction of waves

Wave equation: u_tt = u_xx, Dirichlet boundary conditions

Wave equation: u_tt = u_xx, odd periodic extension

Wave equation: u_tt = u_xx, hammer blow

Dirichlet boundary conditions

Neumann boundary conditions

Movies for Partial Differential Equations

Transport equation: ut + ux = 0

Transport with decay: ut + ux + u = 0

Nonuniform Transport: ut + ux / (x2 + 1) = 0

Nonuniform Transport: ut + (x2 - 1) ux = 0

Nonlinear Transport: ut + u ux = 0, straight line solutions

Nonlinear Transport: ut + u ux = 0, rarefaction wave

Nonlinear Transport: ut + u ux = 0, shock wave

Nonlinear Transport: ut + u ux = 0, initial step function

Heat equation: ut = uxx, Dirichlet boundary conditions

Heat equation: ut = uxx, periodic boundary conditions

Heat equation: ut = uxx, denoising

Wave equation: utt = uxx, particles and waves

Wave equation: utt = uxx, interaction of waves

Wave equation: utt = uxx, Dirichlet boundary conditions

Wave equation: utt = uxx, odd periodic extension

Wave equation: utt = uxx, hammer blow